A framework for sparse matrix code synthesis from high-level specifications

We present compiler technology for synthesizing sparse matrix code from (i) dense matrix code, and (ii) a description of the index structure of a sparse matrix. Our approach is to embed statement instances into a Cartesian product of statement iteration and data spaces, and to produce efficient sparse code by identifying common enumerations for multiple references to sparse matrices. The approach works for imperfectly-nested codes with dependences, and produces sparse code competitive with hand-written library code for the Basic Linear Algebra Subroutines (BLAS).